Thank you for your reply!
Very few tests are available on the net with RDRAND...why?
Here is one:
http://masm32.com/board/index.php?topic=2432.0
Will RDRAND+RDSEED make the error smaller in a Monte Carlo simulation?
RDSEED is interesting but only available in few CPUs yet.
How much better is the RNG in Raspberry Pi compared to the old one (1979...?) in IBM PC?
In general, there does not seem to be much interest (relatively) in things like RDRAND/RDSEED. Hence the relatively little information available about it, compared to other things. I bet many computer people have never heard of it, or even know what it is.
Most things will be fine, with pseudorandom number generators. So they will do fine with a decent, software pseudorandom generator or using the RDRAND instruction.
But a small number of things will benefit from a real hardware true random number generator (such as RDSEED or the one built into the raspberry pi boards hardware). Because of their pure/real mathematical properties. Especially where a huge number of iterations are involved.
I
don't know if Monte Carlo simulations, would benefit or by how much, between a decent pseudorandom number generator, and a real (pure) hardware random number generator.
But suspect you might get at least a small improvement, by using a real hardware random number generator.
Because RDRAND regularly reseeds itself from a real hardware random number generator (and uses a pseudorandom, between those seed updates). It is at least "unpredictable", so can be used for computer security uses, such as encryption. Whereas a purely software based pseudorandom, would still need some method of obtaining "real" random numbers. From time to time, so that it can keep its seed, genuinly random.
Some pseudorandom number software generators do that by using the time in milliseconds (or microseconds) and mice movements and other stuff. To keep the random numbers, somewhat really random. Even though the "pseudorandom" nature of it. Still makes it partially non-random.
There are some tests available, such as "DieHard" random number checker and other, more recent ones.
https://en.wikipedia.org/wiki/Diehard_tests
As regards the original unmodified/upgraded IBM PC. I don't think it ever had a real hardware random number generator built into it. You might be referring to either purely software based pseudorandom number generators, or software which simulates a real hardware random number generator, by looking at the current time and things like mouse movements (earliest IBM PC's did not even have mice, usually, I think). To create an approximation of such a thing, but at an extremely slow data rate.
E.g. As done by some/all Unix and similar Kernels, to create entropy for random number generation.
This link explains about software pseudorandom generators:
https://en.wikipedia.org/wiki/Pseudorandom_number_generator